Let T be an array of size 127 with T[ i ] = i ( T is 0 indexed), In other words T = { 0, 1, 2 ,…….. 126}. Let M be a set of numbers such that:

$M = [ \frac{a_1}{127} + \frac{a_2}{127^2} + \frac{a_3}{127^3} + \frac{a_4}{127^4} \hspace{0.1cm} a_i \in T; \hspace{0.1cm} i=1,2,3,4 ]$

All the numbers in M are arranged in ascending order. Let x be the $20212021^{st}$ term. Answer the nearest integer of $x*10^7$.